Economic mobility in the US is the lowest or 2nd lowest among all OECD nations. I think this means that what anecdotal stories one can tell or find about economic mobility ("Look! Kid from poor impoverished rural town made big bugs as a software developer!" or whatever), the more important reality is that Americans do not move between quartiles or quintiles as much as people in other OECD countries, let alone as much as they like to imagine happens.
[ Edit: as of 2020, the US is roughly middle of the pack for economic mobility among OECD nations, and was not lowest or 2nd lowest, but 4th lowest in 2012 ]
I would caution that "economic mobility" is a term of art that does not mean what most people intuit it to mean, usually conflating it with the ease of improving absolute financial position. You can easily improve your absolute financial position and still have "low mobility", and you can have "high mobility" while having minimal opportunity to improve your financial position. A limitation of economic mobility is that it is only comparable between countries with similar geographic/population size and with similar levels of wage compression. The US is an outlier in all three terms.
Average people want the opportunity to significantly improve their financial position, and economic mobility doesn't measure that. As a country, the US outperforms most other industrialized countries at the former.
Economic mobility doesn't measure relative financial position either. Economic mobility only indicates position relative to a (highly variable) income distribution within a country. A "high" income mobility does not imply high relative changes in financial position, nor vice versa.
At the extreme, very small differences in relative income can make you "highly mobile" even though you've barely moved your relative financial position. This is seen in smaller industrialized countries with very compressed wage distributions. People in low mobility countries can have better financial outcomes in both relative and absolute terms depending on the mathematical distribution function, and do in practice.
The term "economic mobility" is widely used to push misleading narratives precisely because most people don't understand what it measures.
[ Edit: as of 2020, the US is roughly middle of the pack for economic mobility among OECD nations, and was not lowest or 2nd lowest, but 4th lowest in 2012 ]